What should be done to run JDeveloper 11.1.2.1 application on standalone WebLogic 12?
However, I have installed Oracle WebLogic Server 12.1.1 on Oracle Enterprise Linux 6.3 - 64 bit and ADF 11.1.1.2 runtime, so I have installed Oracle Database 11g on another machine.
Moreover, can I use JDeveloper 11g Release 2 (11.1.2.3.0)? Is that better?

No, you can't just run an 11.1.2.x or 11.1.1.x adf application on a 12c wls. You have to install the adf runtime first. Right now (today) there is no adf runtime which can be installed on 12c.
JDev versions need specific wls version with the right runtime installed. Check http://tompeez.wordpress.com/2011/09/14/jdeveloper-versions-vs-weblogic-server-versions/ to find out which versions are possible.

I am writing to Thank for answering my question, so I have another problem.
I have installed standalone Oracle WebLogic Server 11g(10.3.6) and ADF 11.1.1.2 runtime. In addition, I used JDeveloper 11g Release 2 (11.1.2.3.0), yet I wanted to deploy my application for the first time,
I saw this error:
"Please make sure that the annotations are valid. The error is oracle.adf.view.faces.bi.webapp.GraphServlet"

then I created new deployment profile, and I have chosen all libraries. Second time occurred this error:
"Caused by: java.lang.ClassNotFoundException: org.apache.myfaces.trinidadinternal.taglib.UIXSelectItemTag".

Furthermore, do I install patch #14582286 (ADF) and patch #14582309 (WebCenter)? If your answer is yes, please send to me that links.